1) Look at what Atlassian does for automated testing as they build features into JIRA and see if that will apply to what you need. The starting point for that is https://www.atlassian.com/test-automation .

With the tools you are using, the only thing I can think that would come close would be this:

1) Reverse engineer the selenium scripts into test cases and enter them into Zephyr.

2) build a master test cycle, with your new test cases. This will be updated and groomed as the Selenium script evolves.

3) copy that Test Cycle each time you want to run the selenium script.

4)Run your selenium script and use the test results add-on to save the results into your Copied Test Cycle.

5)based on the results, you will have to manually pass/fail the test cases in the test cycle (should take about 5 minutes with the bulk update tool in JIRA). This all can be explained in JIRA TRAINING.